Twisted KK-theory

Twisted complex $K$-theory can be defined for a space $X$ equipped with a bundle of complex projective spaces, or, equivalently, with a bundle of C$^*$-algebras. Up to equivalence, the twisting corresponds to an element of $H^3(X;\Z)$. We give a systematic account of the definition and basic properties of the twisted theory, emphasizing some points where it behaves differently from ordinary $K$-theory. (We omit, however, its relations to classical cohomology, which we shall treat in a sequel.) We develop an equivariant version of the theory for the action of a compact Lie group, proving that then the twistings are classified by the equivariant cohomology group $H^3_G(X;\Z)$. We also consider some basic examples of twisted $K$-theory classes, related to those appearing in the recent work of Freed-Hopkins-Teleman.Comment: 49 pages;some minor corrections have been made to the earlier versio

The Uncertainty of Fluxes

In the ordinary quantum Maxwell theory of a free electromagnetic field, formulated on a curved 3-manifold, we observe that magnetic and electric fluxes cannot be simultaneously measured. This uncertainty principle reflects torsion: fluxes modulo torsion can be simultaneously measured. We also develop the Hamilton theory of self-dual fields, noting that they are quantized by Pontrjagin self-dual cohomology theories and that the quantum Hilbert space is Z/2-graded, so typically contains both bosonic and fermionic states. Significantly, these ideas apply to the Ramond-Ramond field in string theory, showing that its K-theory class cannot be measured.Comment: 33 pages; minor modifications for publication in Commun. Math. Phy

Political masculinities, crisis tendencies, and social transition: Toward an understanding of change

This introduction to the special issue on “Political Masculinities and Social Transition” rethinks the notion of “crisis in masculinity” and points to its weaknesses, such as cyclical patterns and chronicity. Rather than viewing key moments in history as points of rupture, we understand social change as encompassing ongoing transitions marked by a “fluid nature” (Montecinos 2017, 2). In line with this, the contributions examine how political masculinities are implicated within a wide range of social transitions, such as nation building after war, the founding of a new political party in response to an economic crisis, an “authoritarian relapse” of a democracy, attempts at changing society through terrorism, rapid industrialization as well as peace building in conflict areas. Building on Starck and Sauer’s definition of “political masculinities” we suggest applying the concept to instances in which power is explicitly either being (re)produced or challenged. We distinguish between political masculinities that are more readily identified as such (e.g., professional politicians) and less readily identified political masculinities (e.g., citizens), emphasizing how these interact with each other. We ask whether there is a discernible trajectory in the characteristics of political masculinities brought about by social transition that can be confirmed across cultures. The contributors’ findings indicate that these political masculinities can contribute to different kinds of change that either maintain the status quo, are progressive, retrogressive, or a mixture of these. Revolutionary transitions, it seems, often promote the adherence to traditional forms of political masculinity, whereas more reformatory transition leaves discursive spaces for argument